Etibar S. Panakhov

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The inverse nodal problem for the Sturm–Liouville operator is the problem of finding the potential function q and the boundary conditions using the nodal points. The purpose of this paper is to present a method for solving the inverse nodal problem for a singular differential operator on a finite interval. We find asymptotic formulas for nodal points and(More)
In this paper, we give the solution of the inverse Sturm–Liouville problem on two partially coinciding spectra. In particular, in this case we obtain Hochstadt's theorem concerning the structure of the difference q(x) − ˜ q(x) for the singular Sturm Liouville problem defined on the finite interval (0, π) having the singularity type 1 4 sin 2 x at the points(More)
It is well known that the two spectra {λ n } and {µ n } uniquely determine the potential function q (r) in a Sturm-Liouville equation defined on the unit interval having the singularity type () 2 1 2 r r + +   (where  is a integer) at the point zero. In this work, we give the solution of the inverse problem on two partially noncoincide spectra for the(More)
and Applied Analysis 3 and asymptotic formulas for large argument JV (x) = √ 2 πx {cos [x − Vπ 2 − π 4 ] + O( 1 x )} , J 󸀠 V (x) = − √ 2 πx {sin [x − Vπ 2 − π 4 ] + O( 1 x )} . (23) It can be shown [19] that there exists a kernel H(x, t)(?̃?(x, t)) continuous in the triangle 0 ≤ t ≤ x ≤ 1 such that by using the transformation operator every solution of(More)
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